Analysis of Hermite Lossy Nonuniform Transmission Lines Based on Hermite Function and Confluent Hypergeometric Function
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Analysis of Hermite Lossy Nonuniform Transmission Lines Based on Hermite Function and Confluent Hypergeometric Function Yongle Wu & Yuanan Liu & Shulan Li
Received: 19 January 2009 / Accepted: 17 April 2009 / Published online: 12 May 2009 # Springer Science + Business Media, LLC 2009
Abstract The rigorous analytical solutions of the lossy Hermite nonuniform transmission lines (HNTL) are presented in this paper. These solutions are based on two special functions, namely, Hermite function and confluent hypergeometric function. The ABCD matrix of HNTL is given to obtain the corresponding frequency characteristic of the HNTL transformer. Through numerical simulations in different terminated cases, it is found that the lossless HNTL can be matched by resistance loads. This conclusion is different from the lossless one presented by D.torrungrueng. etc. In addition, the distributed power values of HNTL in the lossy case are calculated to show the attenuation character. Keywords Analytical solutions . Hermite tapered nonuniform transmission lines . ABCD matrix . Lossy
1 Introduction In design of microwave and electromagnetic devices, analysis of nonuniform transmission lines [1–9] and novel generalized transmission lines for complex materials [10, 11] is still a research focus and important for impedance matching. Generally, the rigorous analytical solutions of arbitrary nonuniform transmission lines with traditional materials do not exist and the corresponding simulations need some numerical loop computations [3]. However, several kinds of tapered nonuniform transmission lines can be analyzed rigorously by using closed-form functions. For example, the impedance transformation equations for exponential, cosine-squared, and parabolic tapered transmission lines are given in [12], the analytical solution of power-law characteristic impedance transmission lines is presented in [13], and the analytical solutions and analysis of Hermite lines are presented in [14, 15]. Whereas, all the analyzed nonuniform transmission lines in [12–15] are lossless. This paper will extend the single lossless case of [14, 15] to lossy cases using two special functions Y. Wu (*) : Y. Liu : S. Li School of Electronic Engineering, Beijing University of Posts and Telecommunications, P.O.Box.171, 100876 Beijing, China e-mail: [email protected]
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J Infrared Milli Terahz Waves (2009) 30:781–791
which are Hermite complex function and confluent hypergeometric function [16]. To make comparison among the reflection characteristics at different frequencies, the ABCD matrix of HNTL including the lossy case is proposed based on the corresponding analytical solutions. It is necessary to point out that the analytical approach proposed in this paper is different from the approach in [15], which only includes Hermite function and focuses on the lossless case. In fact, when we bring in two different complex functions in this paper, we find the computed values of physical (total) distributed voltages and currents in the lossless case are the same with ones
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